document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257190>Question 257190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the square roots of two numbers is 5. The two numbers differ by 5.<BR>\n" );
document.write( "What are the numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189122 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a be the larger number.<BR>\n" );
document.write( "let b be the smaller number.\r<BR>\n" );
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document.write( "formulas are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29+%2B+sqrt%28b%29+=+5 ALIGN=MIDDLE  ALT=\"sqrt%28a%29+%2B+sqrt%28b%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (first equation)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b+=+5 ALIGN=MIDDLE  ALT=\"a-b+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (second equation)\r<BR>\n" );
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document.write( "use the first equation to solve for a in terms of b.\r<BR>\n" );
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document.write( "first equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29+%2B+sqrt%28b%29+=+5 ALIGN=MIDDLE  ALT=\"sqrt%28a%29+%2B+sqrt%28b%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29+=+5+-+sqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29+=+5+-+sqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "square both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+25+-+10%2Asqrt%28b%29+%2B+b ALIGN=MIDDLE  ALT=\"a+=+25+-+10%2Asqrt%28b%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in second equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+10%2Asqrt%28b%29+%2B+b+-+b+=+5 ALIGN=MIDDLE  ALT=\"25+-+10%2Asqrt%28b%29+%2B+b+-+b+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+10%2Asqrt%28b%29+=+5 ALIGN=MIDDLE  ALT=\"25+-+10%2Asqrt%28b%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract 25 from both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%2Asqrt%28b%29+=+5-25+=+-20 ALIGN=MIDDLE  ALT=\"-10%2Asqrt%28b%29+=+5-25+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "divide both sides of this equation by (-10) to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%29+=+2 ALIGN=MIDDLE  ALT=\"sqrt%28b%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "square both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4 ALIGN=MIDDLE  ALT=\"b+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if b = 4, than a-b = 5 becomes a-4 = 5 becomes a = 9.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "a = 9<BR>\n" );
document.write( "b = 4\r<BR>\n" );
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document.write( "a-b = 5 becomes 9-4 = 5 confirming second equation is true.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29+%2B+sqrt%28b%29+=+5 ALIGN=MIDDLE  ALT=\"sqrt%28a%29+%2B+sqrt%28b%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29+%2B+sqrt%284%29+=+5 ALIGN=MIDDLE  ALT=\"sqrt%289%29+%2B+sqrt%284%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes 3+2 = 5 confirming second equation is true.\r<BR>\n" );
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document.write( "answer is:\r<BR>\n" );
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document.write( "the numbers are 4 and 9.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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